na_lec_7

na_lec_7 - Finite Elements in Two Dimensions The bar truss...

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Unformatted text preview: Finite Elements in Two Dimensions The bar truss structure shown in the figure below consists of 3 bars A , B , C , 3 pins 1,2,3, and two supports. An external force with components and is applied to node 2. The bars are uniform with modulus of elasticity F X F Y F E , cross-sectional area , and length . It is required to find the displacement of the various nodes by using finite element analysis, assuming small deflections. A L X F Y F A B C 1 2 3 A typical element is shown in the figure below. The assumption of small deflection allows us to regards the orientation of the bar at a constant angle θ . The deflections at the two ends of the bar are denoted and , and their components in the x- and y- directions are respectively , , , and v . L w L v R w R L u R u L w R w L u R u L v R v θ The elastic energy stored in the bar is ( ) w K w e T L R w w L EA V ˆ 2 1 2 2 = − = where , and = R L w w w − − = 1 1 1 1 ˆ L EA e K ....
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na_lec_7 - Finite Elements in Two Dimensions The bar truss...

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